Distance, Rate and Time Math Question

Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels
14 miles per hour faster than the eastbound train. If the two trains are 1000 miles apart after 5 hours, what is the rate of the westbound train?

Answer 1

Hi Amber,

 

Sounds like a complicated problem, but we'll take it step by step and all will be clear.

 

First, let's assign the letter x to represent the speed of the slower eastbound train.

 

Next, we can express the speed of the faster westbound bound train as x + 14 (14 mph faster than the slower eastbound train).

 

Next, we can compute the distance each train travels by the distance formula (distance = time x rate). Since we know that each each train traveled the same amount of time (5 hours), we can represent the distance each train traveled as follows:

    miles westbound train traveled:

        time x rate = 5(x + 14)

   miles eastbound train traveled:
        time x rate = 5x

 

Next, we can form our equation by expressing the sum of these distances as 1000 (miles these trains are apart after 5 hours of travel):

    5(x + 14) + 5x = 1000

 

Next, we can solve our equation for x:

    5x + 70 + 5x = 1000

    10x + 70 = 1000

    10x = 1000 - 70

    10x = 930

        x = 930/10

        x = 93 (mph of slower eastbound train)

 

Finally, the answer to our problem:

      x + 14 = 107 (mph of faster westbound train) 

 

The trick to solving these motion problems is to analyze what motion variables are given (rate, time, distance) and then solve for the one that is NOT given.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.